Transition from Hardwood floor to tile

My kitchen has 2 layers of 1/2 inch hardibacker board, thinset, and ceramic tile. The floor has zero-give to it. It meet a "real" oak floor of the same height. the house is on a concrete slab. There is no transition strip between the two, but the grout breaks out easily. Is there a recommendation for a product either grout or special caulk for this? I promised to fix it and can't seem to do it.

Transition tile/wood

Both Mike and Bud are correct. I would go a step further and phone a tile supplier and a wood flooring supplier and get their input. There are new products out there all the time and a flexible wood filler or silicone base caulking should do the trick. Try to match a colour (Canadian spelling), either the wood, tile or surrounding grout.
Good luck.

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Tile /hardwood floor transition

We were told not to use a transition strip there. is that what you mean?
Also, it is between the kitchen and living room so a lot of traffic happens there. I haven't done anything yet, so all options are open. I know the grout has to go cause it is chipping out right now.

i had this same issue and used grout {don't hit me } i knew out the gate it would crack over time but preferred this to caulk only because caulk gets so damn dirty and never quite seems to clean up right.

i did 3 different places this way. so far one has little cracks and 2 don't.

basically i weighed it like this, spend a few minutes once a year mixing grout to fill cracks or having a hard time cleaning caulk